How can I optimize a select query on two dates from a Sqlite DB?

Question

SQLite

Compiled a query to select the maximum values ​​from two fields with dates, using several related tables:

SELECT mes.measureCommFromTab, p.XMLizmerenije, p.XMLdatetime, p.measureComm_id 
FROM `xmlmessagetab` p 
INNER JOIN `indexobjectstab` ps 
ON ps.keyID = p.indexObjectsTab_id 
INNER JOIN `measurecommtab` mes 
ON mes.keyID = p.measureComm_id 
WHERE ps.indexObject = '55285' 
AND p.XMLdatetime = (SELECT max(p.XMLdatetime) 
FROM `xmlmessagetab` p 
INNER JOIN `indexobjectstab` ps 
ON ps.keyID = p.indexObjectsTab_id 
WHERE ps.indexObject = '55285' ) 
AND p.datetimeMess = (SELECT max(p.datetimeMess) FROM `xmlmessagetab` p INNER JOIN `indexobjectstab` ps ON ps.keyID = p.indexObjectsTab_id WHERE ps.indexObject = '55285' )

The query runs for two and a half minutes, which is unbearably long:(
1. Please tell me, is there a way to optimize this query?
2. Is there a plan "B", when writing data to the database, duplicate the last date of the "XMLdatetime" field and then use it for compiling a query for a selection by the latest date, what do you think about this option?