### CONTEXT (Previous Events):
<system_output timestamp="4371.732202">Reading extended state information...
</system_output>
<system_output timestamp="4371.753815">Initializing package states...
</system_output>
<system_output timestamp="4372.190613">Writing extended state information...
</system_output>
<system_output timestamp="4372.440335">Building tag database...
</system_output>
<system_output timestamp="4372.956355">The following NEW packages will be installed:
  ccache gcc-12-base{a} libc6{a} libgcc-s1{a} libhiredis0.14{a} libstdc++6{a} libzstd1{a} 
The following packages are RECOMMENDED but will NOT be installed:
  libidn2-0 
0 packages upgraded, 7 newly installed, 0 to remove and 0 not upgraded.
Need to get 774 kB/4,433 kB of archives. After unpacking 18.3 MB will be used.
Writing extended state information...
</system_output>
<system_output timestamp="4373.009822">... [TRUNCATED TO SAVE SPACE] ...</system_output>
<system_output timestamp="4373.011923">... [TRUNCATED TO SAVE SPACE] ...</system_output>
<system_output timestamp="4373.063244">... [TRUNCATED TO SAVE SPACE] ...</system_output>
<system_output timestamp="4373.108096">... [TRUNCATED TO SAVE SPACE] ...</system_output>
<system_output timestamp="4373.153751">Reading package lists...
</system_output>
<system_output timestamp="4373.390325">Building dependency tree...
</system_output>
<system_output timestamp="4373.393653">Reading state information...
</system_output>
<system_output timestamp="4373.587795">Reading extended state information...
</system_output>
<system_output timestamp="4373.610314">Initializing package states...
</system_output>

### TARGET LINE (Extract and Classify THIS Timestamp):
<system_output timestamp="4374.233851">Writing extended state information...
</system_output>

Answer: 4374.233851, old event